Morphology Evolution in Dealloying

by

Qing Chen

A Dissertation Presented in Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy

Approved February 2013 by the

Graduate Supervisory Committee:

Karl Sieradzki, Chair

Daniel Buttry

Candace Chan

Cody Friesen

ARIZONA STATE UNIVERSITY

May 2013

i

ABSTRACT

Dealloying, the selective dissolution of an elemental component from an alloy, is an

important corrosion mechanism and a technological significant means to fabricate

nanoporous structures for a variety of applications. In noble metal alloys, dealloying

proceeds above a composition dependent critical potential, and bi-continuous structure

evolves “simultaneously” as a result of the interplay between percolation dissolution and

surface diffusion.

In contrast, dealloying in alloys that show considerable solid-state mass transport at

ambient temperature is largely unexplored despite its relevance to nanoparticle catalysts

and Li-ion anodes. In my dissertation, I discuss the behaviors of two alloy systems in

order to elucidate the role of bulk lattice diffusion in dealloying. First, Mg-Cd alloys are

chosen to show that when the dealloying is controlled by bulk diffusion, a new type of

porosity - negative void dendrites will form, and the process mirrors electrodeposition.

Then, Li-Sn alloys are studied with respect to the composition, particle size and

dealloying rate effects on the morphology evolution. Under the right condition,

dealloying of Li-Sn supported by percolation dissolution results in the same bi-

continuous structure as nanoporous noble metals; whereas lattice diffusion through the

otherwise “passivated” surface allows for dealloying with no porosity evolution. The

interactions between bulk diffusion, surface diffusion and dissolution are revealed by

chronopotentiometry and linear sweep voltammetry technics.

The better understanding of dealloying from these experiments enables me to

construct a brief review summarizing the electrochemistry and morphology aspects of

dealloying as well as offering interpretations to new observations such as critical size

ii

effect and encased voids in nanoporous gold. At the end of the dissertation, I will

describe a preliminary attempt to generalize the morphology evolution “rules of

dealloying” to all solid-to-solid interfacial controlled phase transition process,

demonstrating that bi-continuous morphologies can evolve regardless of the nature of

parent phase.

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ACKNOWLEDGMENTS

I could not owe more thanks to my advisor, Dr. Karl Sieradzki, for his mentoring and

help throughout my four years in the group. He equipped me with valuable knowledge,

skills and attitudes that will always be helpful and guiding me in my academic journey.

No matter what direction I will head for, he has made this trip a big appreciation of mine

that I will cherish forever.

I would like to thank Dr. Cody Friesen, Dr. Dan Buttry and Dr. Candace Chan, from

whom I never fail to learn. My labmates Xiaoqian Li, Shaofeng Sun and Elise Switzer

have been great companies to my research and life. I’m also grateful that I can always

receive supports from guys around like Nilesh Badwe, Toni Tang, Jose Bautista, Erika

Engstrom, Jordan Kennedy, Qian Cheng, Andrew Brown and many others I regrettably

can’t list all.

My acknowledgements are also directed to Dr. Peter Crozier for his assistance to the

TEM work, and Dr. Pedro Peralta for serving in my comprehensive committee. There are

so many faculty and staff I’ve interacted with, without the help of whom I wouldn’t be

able to accomplish all my work.

At last, and above all, I would like to thank my parents back in China, for their

unconditional love and support.

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TABLE OF CONTENTS

Page

LIST OF TABLES ........................................................................................................ vii

LIST OF FIGURES ......................................................................................................viii

CHAPTER

1 INTRODUCTION ................................................................................................... 1

1.1 Bi-continuous structure, critical potential and parting limit ................................. 2

1.2 History of dealloying mechanisms ...................................................................... 4

1.3 State of art of dealloying research ....................................................................... 7

2 SOLID-STATE MASS TRANSPORT CONTROLLED DEALLOYING IN MG-CD

ALLOYS....................................................................................................................... 11

2.1 Background ...................................................................................................... 11

2.2 Experiments ...................................................................................................... 15

2.3 Mg0.65Cd0.35 and Mg0.45Cd0.55 dealloying and bi-continuous structure formation 16

2.4 Mg0.10Cd0.90 dealloying and negative dendrite structure formation ..................... 18

2.4.1 Grain orientation dependence of negative dendrites .................................... 20

2.4.2 Current-time behavior for bulk diffusion limited dealloying ....................... 22

2.4.2 Kirkendall voiding during interdiffusion in Mg-Cd .................................... 24

2.5 Conclusions and remarks .................................................................................. 25

3 DEALLOYING IN LI ALLOYS ........................................................................... 27

3.1 Background ...................................................................................................... 27

v

CHAPTER Page

3.2 Experiments ...................................................................................................... 28

3.2 Aqueous dealloying of Li alloys and bi-continuous structure formation............. 29

3.3 Composition dependent morphology in dealloying Li-Sn alloy ......................... 30

3.4 Particle size dependent morphology in Li-Sn alloy ............................................ 32

3.5 Dealloying rate dependent morphology in Li-Sn alloy....................................... 34

3.6 Grain boundary formation during lithiation / de-lithiation ................................. 37

3.7 Improving Sn anode cycle stability by nanoporous structure ............................. 38

3.7 Conclusions ...................................................................................................... 40

4 DEALLOYING THEORY: REVISITED............................................................... 41

4.1 Critical behaviors in dealloying ......................................................................... 41

4.1.1 Passivation ................................................................................................. 42

4.1.2 Parting limit ............................................................................................... 43

4.1.2 Critical potential......................................................................................... 45

4.1.3 Critical electrode size ................................................................................. 47

4.2 Morphology characteristics ............................................................................... 49

4.2.1 Theoretical background .............................................................................. 49

4.2.2 Length scales in bi-continuous structures ................................................... 51

4.2.3 Ligament collapsing ................................................................................... 53

4.2.4 Volume change .......................................................................................... 55

vi

CHAPTER Page

4.2.5 Encased voids ............................................................................................ 56

5 FROM DEALLOYING TO DECOMPOSITION ................................................... 58

5.1 Background ...................................................................................................... 58

5.2 The formula of bi-continuous structure evolution from decomposition .............. 58

5.3 Experimental .................................................................................................... 60

5.4 Results and Discussion...................................................................................... 60

6 CONCLUSIONS ................................................................................................... 65

REFERENCES.............................................................................................................. 67

vii

LIST OF TABLES

Table Page

4.1 Parting limits for various alloys ............................................................................. 44

4.2 Data used in Fig. 4.2 .............................................................................................. 52

viii

LIST OF FIGURES

Figure Page

1.1 Nanoporous metals prepared by dealloying (a) Ag-Au, (b) Mn-Cu and (c) Stainless

steel 316. The scale bars are 200 nm .......................................................................... 2

1.2 Polarization curves of Ag-Au alloys in 1 M AgClO4 +1 M HClO4 solution (4). The

scan rate is 1 mV/s ..................................................................................................... 3

1.3 Cartoons of dealloying mechanisms for (a) dissolution and re-deposition (Cu-Au), (b)

solid-state bulk diffusion(17), and (c) surface diffusion (Ag-Au)(18) ......................... 5

1.4 Illustration of the dealloying theory based on percolation......................................... 6

1.5 Statistics of the citation number for “Evolution of nanoporosity in dealloying”. For

the corrosion part, only publications from electrochemical journals (such as J.

Electrochem. Soc. and Corr. Sci.) are included to roughly eliminate those applying

the corrosion process for nanostructure fabrication. All data is from Web of Science . 8

2.1 Mechanisms of dealloying (a) above and (b) below percolation threshold. ............. 13

2.2 Mg-Cd phase diagram (with chosen compositions labeled)(47) .............................. 14

2.3 EDS, XRD and polarization data for (a, c, e) Mg0.65Cd0.35 and (b, d) Mg0.45Cd0.55 .. 17

2.4 Dealloyed Morphologies of (a, c) Mg0.65Cd0.35 and (b, d) Mg0.45Cd0.55. The scale bars

are 10 um................................................................................................................. 18

2.5 EDS, XRD and polarization data for Mg0.10Cd0.90 .................................................. 19

2.6 Cross-section views of Mg0.10Cd0.90 dealloyed at various conditions: (a) 50C for

10000s; (b) 150C for 10000s; (c) 210C for 5000s; (d) 210C for 10000s. The scale

bars are 1um. ........................................................................................................... 20

ix

Figure Page

2.7 Correlation of EBSD results and negative dendrite morphologies obtained by

dealloying the Mg0.10Cd0.90 alloy: (a) EBSD results for a section of the planar surface

showing grain orientations by color indicated in the standard triangle. Scale bar

600um; (b-d) FIB milled cross-sections of the three grains labeled in a, with lattice

orientations illustrated as insets. Scale bars are 400 nm. (e) Cartoon illustration of

negative dendrite morphology evolution for the grain orientation shown in image b. 21

2.8 Current decay curves for dealloying of Mg0.10Cd0.90 at different temperatures, with

fitted lines in black. The inset is as-interpolated curve of Mg chemical diffusion

coefficient vs. reciprocal temperature ...................................................................... 24

2.9 Cross-section view of the bilayer sample annealed in the Kirkendall voiding

experiment. The scale bar is 1 um ............................................................................ 25

3.1 Bi-continuous nanoporous morphologies resulting from free corrosion de-lithiation

of Sn, Pb, Cd and Bi reservoirs in an aqueous electrolyte. The scale bars in the images

are 2 µm. ................................................................................................................. 30

3.2 (A) voltage-composition curve for Li-Sn modified from a C/20 charging curve. SEM

images and FIB cross-sections of (B, C) Li0.30Sn0.70, the inset is the magnified cross-

section by 2 times; (D, E) Li0.48Sn0.52; (F, G) Li0.77Sn0.23. The scale bars are 500nm. 31

3.3 The effect of particle size on dealloyed morphologies ............................................ 33

3.4 Bi-modal porous Sn sheet obtained after two potentiostatic cycles ......................... 34

3.5 (A, B) chronopotentiometry curves and (C, D) polarization curves without and with

normalization, respectively ...................................................................................... 35

x

Figure Page

3.6 (A~D) Sn particles dealloyed at rates of 10C, C/1, C/2 and C/10 respectively; (E)

particle dealloyed at fixed potential of 0.5V; (F) cartoons illustrate the morphology

evolution at different rates, with the coloring for different alloy compositions. ........ 37

3.7 Grain size comparisons between virgin Sn substrates and Sn after lithiation / de-

lithiation circle for (a, b) Sn particles, and (c, d) Sn sheets. The particle in (b) was

lithiated to 0.6V and de-lithiated at 2.5V, and the sheet in (d) was lithiated at 0.2V

and de-lithiated at 1V .............................................................................................. 38

3.8 Capacity retention tests for different Sn particle electrodes .................................... 39

4.1 (A) cartoon illustrating the difference between planar and particulate alloys, with

dotted lines denoting the effective areas for dissolution and surface diffusion,

respectively; (B) critical size effects on porosity formation in Pt and Au alloys ....... 48

4.2 Ligament size and homologous temperature correlation for porous metals ............. 52

4.3 (A) Rayleigh instability in porous metals; (B) ligament collapsing mechanism at the

grain boundary, with ligaments susceptible to collapsing circled in blue; (C) and (D)

NPG with collapsed ligaments after 10 mins and 1 h annealing at 500C, in which the

collapsing starts at grain boundaries and grow on the surface. The scale bars are 40um

................................................................................................................................ 53

4.4 Volume change in dealloyed Li-Sn alloys .............................................................. 55

4.5 (A) Encased voids in NPG and (B, C) EELS scans across voids indicating

significantly higher counts of oxygen signals inside the voids .................................. 57

5.1 Compounds before de-composition reaction, (a) AgO; (b) SnS; (c) Ag2S (adjacent to

a cross-section); (d) CuSO4 ...................................................................................... 61

xi

Figure Page

5.2 Decomposed (a, b) AgO and (c) SnS...................................................................... 62

5.3 Decomposed Ag2S ................................................................................................. 63

5.4 Decomposed (a) CuSO4*5H2O, (b) PbCO3 ............................................................ 64

1

1 INTRODUCTION

Components in an alloy can be selectively dissolved owing to the chemical property

difference, a process long known as dealloying. Research on dealloying dates back to the

1920s(1, 2), when people were more concerned about its role in alloy corrosion.

Dealloying process, if present, will determine an alloy’s corrosion resistance, therefore

various systems were examined with respect to their electrochemical responses, either for

the alloy’s practical importance, such as Zn-Cu and Al-Cu, or for its simplicity like Ag-

Au and Cu-Au(3–5). Dealloying is also considered the cause for certain types of stress

corrosion cracking, because the dealloyed layer is mechanically weak and injects crack

into the alloy(6, 7). This layer, owing to the development of characterization tools, was

later observed to be beautifully nanoporous, and the porous structure is bi-continuous

meaning that both the void space and the solid ligaments are continuous throughout the

whole material (see Figure 1.1 for examples). This observation quickly shifted the center

of dealloying research towards its more desirable role in nanostructure fabrication.

Because of its high surface area and metallic nature, the dealloyed structure is attracting

more attention in a wide range of applications, including catalysts(8), sensors(9),

actuators(10), and radiation damage resistant materials (11).

2

Figure 1.1 Nanoporous metals prepared by dealloying (a) Ag-Au, (b) Mn-Cu and (c)

Stainless steel 316. The scale bars are 200 nm

1.1 Bi-continuous structure, critical potential and parting limit

These are the three key features accompanying dealloying. As mentioned earlier, the

bi-continuous porous structure evolves naturally during dealloying. The ligaments are

composed mainly by the more noble component, and their diameter, ranging from a few

nanometers to micrometers; controllable either in-situ (during dealloying) or by post-

annealing(12).

The other two features can be best seen in polarization curves. These curves are either

obtained by simply sweeping the potential from low to high, or constructed by obtaining

the steady-state current density at fixed potentials(13). Fig. 1.2 is a typical plot of a group

polarization curves for different Ag-Au alloys. Ag-Au has always been the most popular

system for dealloying study, due to its simplicity. This simplicity includes the full

composition range of solid solution phase, the large difference in the standard potential of

Ag and Au, and the relatively simple electrochemistry of both components in aqueous

electrolyte. As shown in Fig. 1.2, compared to pure less noble metal’s dissolution

potential (0 mV), dealloying always turns-on at a much higher overpotential, which is the

so-called critical potential. Below this potential, dealloying is usually limited to a thin

3

surface layer(14), and above it, dealloying behaves qualitatively like elemental metal

dissolution but results in bi-continuous structures. The value of critical potential cannot

be explained by the activity of the less noble component in the alloy, which comprises

only a very small portion of the overpotential with respect to the standard potential of the

element dissolving. The critical potential also increases with decreasing less noble

component content, until reaching an alloy composition for which dealloying can no

longer proceed. This lower bound of less noble component content for dealloying is

termed as parting limit. For Ag-Au, this parting limit is about 55 at% Ag(4).

Figure 1.2 Polarization curves of Ag-Au alloys in 1 M AgClO4 +1 M HClO4 solution

(4). The curves from low to high voltage are in the exact same sequence as for increasing

Ag contents. The scan rate is 1 mV/s

4

1.2 History of dealloying mechanisms

To explain the kinetics behind dealloying has always been a complicated but

fascinating task. Various mechanisms have been proposed, and are summarized with the

drawings in Fig. 1.3 and 1.4. The model eliminated most easily is “dissolution and re-

deposition”. It proposes that during dealloying both components of a binary alloy are

dissolving simultaneously and the more noble component re-deposits in a form of porous

structure. This speculation can be tested by a rotating-ring-disk electrode (RRDE)

experiment, which was conducted by Pickering and Wagner in 1967(15). They used a

Cu-Au alloy as the disk and during its dealloying no Au reduction was detected on the Pt

ring.

In the same work, Pickering and Wagner proposed another possible mechanism of

dealloying based on solid-state bulk diffusion. Under this mechanism, the more noble

component builds up a surface layer isolating the dissolving component from the

electrolyte, and dealloying needs to proceed by bulk diffusion through the layer. However,

mono-vacancy diffusion in all examined alloy systems is too slow by tens of orders of

magnitudes to support dealloying(16). Therefore, they turned to a bulk diffusion path via

di-vacancies. This type of diffusion usually happens at relatively high homologous

temperature (TH, experimental temperature divided by metal or alloy melting point), so an

associated assumption was that large amount surface vacancies from dealloying would be

injected to the bulk to facilitate the bulk diffusion. Regardless of the validity of this

controversial assumption, the bulk diffusion flux calculated was still orders lower than

that measured in dealloying. Moreover, to achieve 1 mAcm-2

current density which is

5

routinely obtained during dealloying of Cu-Au and Ag-Au, the surface mole fraction of

di-vacancy needs to unrealistically approach 1. All the key dealloying features discussed

in the previous session cannot be explained by this mechanism either - especially the

morphology. As shown in Fig. 1.3b, if the dealloying is carried out by bulk diffusion, the

alloy surface will develop wedges later turned into “trees” but with no connectivity to

each other.

Figure 1.3 Cartoons of dealloying mechanisms for (a) dissolution and re-deposition (Cu-

Au), (b) solid-state bulk diffusion(17), and (c) surface diffusion (Ag-Au)(18)

On the other hand, atoms on the surface have no difficulty diffusing around. In fact,

the dealloying process must involve a high degree of surface diffusion for its production

of a large number of adatoms and atoms at defect sites, or phrased in the larger scale,

features with high curvature that need to be smoothened to lower the surface energy. The

clear correlation between surface diffusion and the dealloying morphology was

established when Forty(18) reported for the first time bi-continuous structures by

dealloying Ag-Au alloy. In the work, he characterized the morphology evolution along

with increasing dealloying time and post-annealing time, showing that the 2-dimentional

6

“maze”-like islands enlarge at their edges into an interconnected network. Based on this

observation, he suggested a surface diffusion controlled mechanism illustrated in Fig.

1.3c. The dealloying starts with surface Ag dissolution, leaving Au atoms diffusing into

growing Au island; this surface diffusion process in turn exposes more Ag to the

electrolyte, which advances the dissolution layer by layer. This scenario successfully

visualizes the morphology evolution during dealloying and becomes a basis for the

understanding of dealloying.

However, with surface diffusion alone, it is difficult to give quantitative or even

intuitive explanations to dealloying features like critical potential and parting limit. The

piece missing is to describe the alloy at the moment right before the dissolution, when

both types of atoms are still in the matrix, because the atom neighbors will definitely

affect the probability of a specific dissolution event. This problem was solved when

percolation theory was introduced by the works of Sieradzki and Newman(19, 20). As far

as dealloying in noble metal alloys is concerned, the percolation theory is capable of

explaining most observations, and will also be the base of my dissertation.

Figure 1.4 Illustration of the dealloying theory based on percolation

7

To apply percolation theory to dealloying, we start with a close-to-ideal binary solid

solution alloy ApB1-p. The bulk material can be viewed as two types of atoms randomly

distributed inside a crystal matrix. As percolation theory states, once a component’s

content is above a percolation threshold (pc), the atoms of the same kind will form

continuous clusters via near neighbor bonding throughout the whole material(21).

Therefore when p is above pc, the clusters of less noble component A will serve as the

pathways for electrolyte to follow which sustains the dissolution, and p=pc sets the

ground for the parting limit. When 1-p is above pc, the remaining B clusters become the

continuous backbone for the evolving porous structure. The average A cluster size will be

composition dependent. Small as it always is, the cluster’s dissolution requires an extra

overvoltage from the associated Gibbs-Thompson term, and this is reflected in the

magnitude of the critical potential(4, 22). Although in most cases, surface diffusion

causes the real dealloying process to deviate from the ideal prediction, the three key

features of dealloying are well explained collectively by the mechanism in systems like

Ag-Au(4, 22).

1.3 State-of-the-art of dealloying research

The present picture of dealloying related research can be roughly drawn by

constructing a citation report of a 2001 paper titled “Evolution of nanoporosity in

dealloying”(23), which is the most cited paper on the topic. As shown in Fig. 1.5, while

the alloy corrosion part of dealloying remains steady over the years, the total number of

citations increases exponentially owing to the increasing interests in the nanostructures.

One major contributor is catalysis research, which at the year of 2012 made up more than

8

one third of the overall citations. Among these exist two main directions with quite

different concerns: one is using the process to achieve high surface area(8, 24); the other

is applying the theory to explain the instability of alloy catalysts(25), which can, though

rarely, be categorized as alloy corrosion.

Figure 1.5 Statistics of the citation number for “Evolution of nanoporosity in dealloying”.

For the corrosion part, only publications from electrochemical journals (such as J.

Electrochem. Soc. and Corr. Sci.) are included to roughly eliminate those applying the

corrosion process for nanostructure fabrication. All data is from Web of Science

The types of alloys undergoing the most studies are still those containing at least one

noble metal component. To obtain nanoporous structures, base metals such as Al(26),

Ni(8) and Co(27) are often chosen as the dissolving species to reduce costs; multiphase

alloys(28), nonequilibrium alloys(29) and amorphous alloys(30) have also been studied

to broaden the applicability of this synthesis process. The most popular more noble

component for dealloying is undoubtedly Pt, due to its supreme catalytic ability towards

9

various reactions such as oxygen reduction(8). At the same time as precious metals’

prices soar, downsizing the alloy electrodes becomes a major trend of dealloying. This

gives rise to a group of new morphologies that are never seen in bulk electrodes,

including core-shell structures and hollow structures(27, 31).

Along with the experimental works, computer simulation is also playing a big role in

dealloying research. The most common approach is Kinetic Monte Carlo (KMC), which

was performed as early as 1980 by Sieradzki et al.(19) and then improved by the works

of Erlebacher(23, 32–34). The coding visualizes dissolution and surface diffusion

processes, with controllable parameters like voltage and bonding energy, which is able to

reproduce all the key features discussed in session 1.1. Meanwhile, because kinetic

events during dealloying elapse too quickly to be captured experimentally, KMC has

been a great complement for both analysis(32) and prediction(35). Other simulation tools

are not so often employed, but have shown potentials towards specific problems in

dealloying such as ligament stability(36) and surface dealloying(37).

All the extensive works discussed above are in systems that display negligible lattice

diffusion at the experimental temperature, such as noble metal alloys at ambient

temperauter. In contrast, dealloying of systems with considerable ambient solid-state

diffusion remains virtually unexplored. It will be of fundamental interests to understand

the role of bulk diffusion when it actively participates the dealloying. In addition, there

are two practically significant issues tightly linked to this type of dealloying. The first

issue is in nanoparticles of small enough size to involve melting point depression thus

increasing bulk diffusivity(38, 39). The second is with Li alloys, which are considered as

future Li-ion anodes. In those alloys, the bulk diffusion process is known to be fast even

10

at room temperature(40), and surprisingly, there has yet been any comprehensive works

with respect to morphology evolution and the electrochemical parameters affecting this

process.

In this dissertation, I will first attempt to answer the question of how the bulk

diffusion affects the dealloying process and its morphology evolution. In Chapter 2, the

close-to-ideal Mg-Cd alloy system is explored to show that a new kind of morphology, i.e.

negative void dendrite, evolves when dealloying is under bulk diffusion control. Chapter

3 is centered on Li containing alloys. Depending on the alloy composition, electrode size

and dealloying rate, bi-continuous structures evolve as well as other known dealloying

morphologies. Based on the works in Chapter 2 and 3, and all the contributions from

colleagues to dealloying research, a brief review will be constructed with the focus on

electrochemical behaviors and morphology evolution of dealloying across all the alloy

systems examined to date. At last, Chapter 5 presents initial efforts to extend the theory

of dealloying beyond purely metallic systems, by showing the bi-continuous structure can

evolve in any interfacial controlled selective dissolution process.

11

2 SOLID-STATE MASS TRANSPORT CONTROLLED DEALLOYING IN MG-

CD ALLOYS

2.1 Background

As mentioned in the previous chapter, solid-state bulk diffusion was initially

considered as one possible mechanism to support ambient temperature dealloying.

Following an approach analogous to that adopted by Wagner in developing analytical

models for high temperature oxidation(41), Pickering and Wagner developed a model of

ambient temperature dealloying of Zn-Cu and Cu-Au alloys by assuming that diffusion

was supported by a di-vacancy mechanism(15). In order to account for the

experimentally measured large dealloying fluxes, they had to assume the existence of

abnormally high concentrations of excess di-vacancies during dealloying, for instant, a

mole fraction of di-vacancies of order 10-2

for a dealloying current density of 10-4

Acm-2

,

and of order 1 for 10-3

Acm-2

. These current densities and higher are easily obtained, and

we note that the alloy compositions considered by these authors were already above

percolation thresholds therefore solid-state mass transport was not required for dealloying

these systems. There are other works where dealloying were carried out under conditions

of significant bulk diffusion, including Ag-Au alloys at 800C(42) and In-Sn alloys at

room temperature(43), but the lack of characterization tools greatly limited their

completeness.

In order to address the issue of morphology evolution in an alloy when the rate-

limiting step (RLS) for dealloying is solid-state mass transport it will be necessary to

consider two conditions with respect to alloy composition and elemental site occupation.

First, as described in the introduction, for the case of single phase solid solution alloys

12

the composition of the dissolving species must be below the site percolation threshold of

the lattice network, otherwise continuous nearest neighbor pathways are available to

support dealloying. Second, in typical metal alloys where the lattice sites are almost fully

occupied and the interstitial site occupation is dilute, the alloy component being dissolved

must occupy the lattice sites in the crystal structure of the alloy. On a thermodynamic

basis, for these alloys the interstitial components can be treated as “fluids” within the

solid network in the sense that the dissolution or accretion of such a component from the

surface leaves the number of lattice sites unchanged(44) and does not result in the

creation of surface vacancy. In more complicated crystal structures where site occupancy

for both the lattice and interstitial sites is high, the interstitial vacancies can be treated as

solid components in a thermodynamic sense and dealloying could still result in vacancy

creation(45). We briefly discuss one possible example at the end of this chapter.

The morphology evolution by bulk diffusion controlled dealloying can be discussed

under the rule of phase transformation kinetics and interface stability to perturbations first

identified by Wagner(41). This simple rule is applicable to a variety of “growth”

processes including elemental metal and alloy solidification, oxidation, electropolishing

and electrodeposition. Within the context of electrochemical dealloying consider the

growing phase to be the electrolyte and the shrinking phase to be the parent phase alloy.

If the rate-limiting step (RLS) is in the shrinking phase, a planar alloy/electrolyte

interface will be unstable to perturbations that will tend to grow in magnitude as time

evolves, whereas if the RLS is in the growing phase the planar interface will be stable.

Consider an ApB1-p binary alloy in which A is the dissolving component and B is

“insoluble” in the electrolyte. Figure 2.1 depicts the expected dealloyed morphologies at

13

compositions above and below the site percolation threshold of component A. Above the

percolation threshold, even if the solid-state diffusivity of component A is large,

dealloying will still be under interface control and the dealloyed morphology will be bi-

continuous. At compositions below the percolation threshold selective dissolution of the

A component can only proceed by a process involving the mass transport of A from the

interior of the alloy to the alloy/electrolyte interface. For every A atom dissolved from a

terrace site on the interface a vacancy is formed at that location. Such a dissolution

process is isomorphic to a diffusion-limited aggregation (DLA) processes. Thus we

expect to observe a dealloyed morphology consisting of negative tree-like structures or

“void-dendrites” penetrating into the solid. In analogy with normal dendritic growth the

detailed shape evolution of these negative dendrites will reflect the anisotropy in

interfacial energy defined by the crystal lattice structure of the now dealloyed parent

phase.

Figure 2.1 Mechanisms of dealloying (a) above and (b) below percolation threshold.

In this chapter, Mg-Cd alloy system is chosen for the following reasons. Unlike

noble-metal-containing alloys, Mg-Cd alloys have relatively low melting points over the

entire compositional range (Figure 2.2) which guarantee high bulk diffusion rates at or

14

near ambient temperatures. They form a series of hexagonal close packed (HCP) based

structures that minimizes the crystal structure change during dealloying. In addition, the

Mg-Cd system was one of the early systems for which the Kirkendall effect was

examined so that there exists data for the chemical interdiffusion coefficients(46), which

will helpfully guide our theoretical analysis.

Figure 2.2 Mg-Cd phase diagram (with chosen compositions labeled)(47)

15

2.2 Experiments

Mg-Cd alloys were supplied by the Ames Laboratory. The three compositions (at %)

used here are Mg0.65Cd0.35 (D019 structure; melting temperature, 743 K), Mg0.45Cd0.55

(B19 structure; melting temperature, 698 K) and Mg0.10Cd0.90 (random hcp structure;

melting temperature, 613 K). Elemental Mg and Cd (99.9% purity) were purchased from

Alfa Aesar. All electrodes were mechanically polished to 1200 grit with hexane as a

lubricant, except Mg0.10Cd0.90, which was further electropolished in H3PO4-glycol-water

(2:2:1 in volume ratio) solution(48).

The composition and crystal structure of the alloys were checked by X-ray

Diffraction (XRD) and Energy Dispersive X-ray Spectroscopy (EDS). Wet chemical

analysis was adopted to verify the EDS results.

Dealloying of Mg was performed in either Choline Chloride-Urea (ChCl-Urea) ionic

liquid (iL) or 1-Butyl-3-MethylImidazoliumm bis-Trifluoromethylsulfonate (BMImTfSI).

The ChCl-Urea was prepared by mixing ChCl (Alfa Aesar, 95+%) and Urea (EMD, 99%)

in 1:2 molar ratio. Prior to the electrochemical experiments, both iLs were deaerated in an

MBraun glovebox, until the water content was below 100 ppm for ChCl-Urea, and 1ppm

for BMImTfSI (EMD), tested by Karl-Fischer titration (Mettler Toledo model C20).

The dealloying experiments were performed in an Ar-deaerated three-electrode cell

using a Gamry Series G potentiostat. Platinum mesh was used as the counter electrode

and a Cd wire, with pre-dissolved ~10-4

mol/L Cd2+

served as a pseudo reference

electrode. The potential stability of this reference was ± 50mV over the duration of the

16

experiments. For all experiments dealloying was performed at -100mV vs. the reference

electrode, for time periods ranging from 1000~10000s.

In the ancillary Kirkendall voiding experiment, a 500 nm thick layer of Cd,

mimicking the dealloyed Cd-rich layer, was electrodeposited on to an electropolished

Mg0.10Cd0.90 alloy surface from an aqueous electrolyte containing 0.1M CdSO4 (Fluka,

99.9%) and 1mM NH4OH (Sigma Aldrich, 28~30%). The sample was then annealed at

210 C (TH = 0.618) for 10000 s in an atmosphere containing 5% H2 + 95% Ar.

During Focused Ion Beam (FIB) cross-section milling, there was always a 100 to

500nm platinum layer deposited by the gallium ion beam to protect the top surface. The

cross-section images were taken with a 52 degree angle versus the horizontal plane,

meaning a ~1.62x correction to the depth-direction length measurement in the images.

FIB, Scanning Electron Microscopy (SEM) and EDS were all conducted in FIB/SEM

Nova 200 NanoLab UHR FEG (FEI) system. XRD spectra were obtained by PANalytical

X’Pert Pro Materials Research X-ray Diffractometer with a Cu Kα source. Electron

Backscatter Diffraction (EBSD) experiments were performed in FEI XL30 SEM system.

2.3 Mg0.65Cd0.35 and Mg0.45Cd0.55 dealloying and bi-continuous structure formation

As a routine for all Mg-Cd alloys employed, EDS, XRD and electrochemical

polarization were applied to verify alloy properties. In Figure 2.3, EDS and XRD results

show both alloys are of the nominal composition and crystal structure; Figure 2.3e is a

typical polarization curve for high Mg content alloy, whose oxidation potential sits

between elemental Mg and Cd.

17

Figure 2.3 EDS, XRD and polarization data for (a, c, e) Mg0.65Cd0.35 and (b, d)

Mg0.45Cd0.55

The reason why we used ChCl-Urea in high Mg content alloy dealloying is due to the

existence of a robust oxide on the alloy surface. BMImTfSI is not able to dissolve it and

the dealloying results in highly localized pits, whereas ChCl-Urea yields a clean

dealloyed surface. After dealloying, the electrode surface was quickly washed with water

and isopropanol. Both alloys’ dealloying resulted in the evolution of uniform bi-

continuous porous structures, as shown in Figure 2.4. The length scale of the bi-

continuous morphology for the 65at% Mg alloy ranged from ~4 to 10µm which is

considerably larger than that found in the room temperature dealloying of noble face-

centered cubic alloys such as Ag-Au(12). This larger length-scale is a result of the high

homologous temperature (TH ~0.50) at which these experiments were carried out.

Consequently Ostwald ripening of the ligaments is significantly enhanced by surface

mass-transport processes(12). The length scale of the bi-continuous morphology for the

45 at% Mg alloy is ~ 2 µm and at this composition there are no comparisons to be made

to dealloying in noble FCC alloys as this composition is below the so-called parting limit

18

of such alloys(19). In fact to our knowledge, this is the first demonstration of bi-

continuous porosity evolution in a binary alloy at this composition, and we will re-visit

the concept of parting limit in Chapter 4.

Figure 2.4 Dealloyed Morphologies of (a, c) Mg0.65Cd0.35 and (b, d) Mg0.45Cd0.55. The

scale bars are 10 um

2.4 Mg0.10Cd0.90 dealloying and negative dendrite structure formation

As shown in Figure 2.5, Mg0.10Cd0.90 started with the designated composition, crystal

structure and electrochemical property. For this alloy, dealloying was carried out in the in

the BMImTfSI iL for three reasons. First this iL has a much higher decomposition

temperature which allowed us to examine dealloying over a wider range in homologous

19

temperature. Second this iL has a larger electrochemical stability window and a thin

cadmium-rich oxide film is preserved (retained from electropolishing) on the surface of

this alloy that serves to sufficiently quench surface diffusion processes that might

otherwise obscure or alter the dealloyed morphology. We note that the Mg content in this

alloy is well below the 20 at% site percolation threshold for the hcp crystal structure(49).

Figure 2.5 EDS, XRD and polarization data for Mg0.10Cd0.90

Figure 2.6 shows FIB cross-section images of the dealloyed morphologies in

Mg0.10Cd0.90 at different dealloying temperatures, for varying times. At 50C (TH = 0.527)

it was difficult to discern dealloying features, which were likely too shallow in depth. At

TH = 0.690, significant DLA/dendrite-like structures are apparent owing to the higher Mg

diffusivity. Unlike bi-continuous porous structures, the void-dendrite branches do not

merge into one another. This is a consequence of the depletion in Mg that occurs in

regions between the dendrites and the inability of significant amounts of Mg to diffuse

20

into these regions as the Mg diffusers are captured by the tips of the growing dendrites. In

spite of significant coarsening, there is distinguishable side branching and accordingly

some level of self-similarity to the morphology of these structures. At a temperature of

TH = 0.788, deeper growth is observed within the same period of time. At this

temperature these structures coarsen more quickly and are consequently not as narrow,

however, fractal-like features of this morphology are more apparent.

Figure 2.6 Cross-section views of Mg0.10Cd0.90 dealloyed at various conditions: (a) 50C

for 10000s; (b) 150C for 10000s; (c) 210C for 5000s; (d) 210C for 10000s. The scale bars

are 1um.

2.4.1 Grain orientation dependence of negative dendrites

Similar as positive dendrites by deposition, negative dendrites display preferential

growth, rooted from the anisotropy of the parent alloy. Prior to dealloying Electron

21

Backscatter Diffraction (EBSD) was used to determine grain orientations in order to

assess this issue. Figure 2.7 shows FIB-milled cross-sections of the dealloyed structures

for three adjacent grains (orientations are indicated in Figure 2.7a, with colors

corresponding to the Miller index in the sector plot).

Figure 2.7 Correlation of EBSD results and negative dendrite morphologies obtained by

dealloying the Mg0.10Cd0.90 alloy: (a) EBSD results for a section of the planar surface

showing grain orientations by color indicated in the standard triangle. Scale bar 600um;

(b-d) FIB milled cross-sections of the three grains labeled in a, with lattice orientations

illustrated as insets. Scale bars are 400 nm. (e) Cartoon illustration of negative dendrite

morphology evolution for the grain orientation shown in image b.

We observed that the dendrites were mainly aligned along the basal plane for each of

the grain orientations. This is similar to the orientation-dependent pitting corrosion in

Cd(48) and Mg(50, 51). Although the details of the kinetics of pitting and negative

dendrite formation are different, we attribute our dendrite orientations to the same cause

as that observed in the pitting corrosion of elemental Cd and Mg – the anisotropy of

surface energy. In the hcp structure, the basal plane has the lowest surface energy(52, 53).

The dendrite surface orientations evolve by surface diffusion and the driving force for

this is the minimization of the interfacial energy. Figure 2.7C is an illustrative cartoon

22

showing how the combination of dealloying and surface diffusion acts to evolve these

directionally anisotropic void-dendrite structures.

2.4.2 Current-time behavior for bulk diffusion limited dealloying

During dealloying, the measured current density follows t-1/2

kinetics. Both the

dealloyed morphology and the kinetics of dealloying provide strong evidence for solid-

state mass transport control of dealloying at the Mg0.10Cd0.90 alloy composition.

Evaluation of the growth rate of these DLA-like structures from the measured current-

time behavior is exceptionally complex, as this is a fully non-linear three-dimensional

diffusion problem and likely only amenable to solution using numerical techniques.

Nevertheless, considerable insight can be drawn from a simple one-dimensional solution

incorporating a moving alloy/electrolyte boundary.

Following Pickering and Wagner(15) we consider diffusion normal to the initial

alloy/electrolyte interface and at time zero that the initial concentration of Mg, c0

(mol/cm3), is uniformly distributed within the bulk of the alloy. The flux of Mg atoms at

the instantaneous position, zi of the interface is given by ⁄ , and the

concentration of Mg atoms at the interface is taken to be zero. The interface velocity

given by

⁄ ⁄ 2-1

where Vm is the molar volume of Mg in the alloy and D is the diffusivity. Under the

stated initial and boundary conditions a solution to the time dependent diffusion equation

2-2

is given by,

23

⁄ 2-3

⁄ ⁄ 2-4

where α is a constant determined by substitution of Equation 2-3 and 2-4 into Equation 2-

2 as

⁄ 2-5

The magnitude the A flux at the instantaneous position of the alloy/electrolyte

interface is given by,

⁄

⁄ 2-6

and the dealloying current density is

⁄ 2-7

For the alloy compositions considered by Pickering and Wagner, p was near unity and

consequently they employed a series expansion for the erfc function in order to determine

. For the composition (p = 0.1) of interest here we evaluate numerically from

Equation 2-5 to be 0.06. Then we obtain,

⁄ 2-8

This analysis assumes that the chemical diffusivity is independent of composition

over the relevant range in Mg concentration (0~10 at%). We have fit the current decays

to this form of the current density and obtained the diffusivities of Mg at different

temperatures. Figure 6 show the results versus reciprocal temperature and the activation

enthalpy obtained for Mg diffusion. These values for the diffusivity are lower by about a

factor of three than those obtained from Kirkendall interdiffusion experiments(46) but the

activation enthalpy is within 10% of that found in those measurements. Over the time

24

scale of our experiments the mean velocity of the solid/electrolyte interface is of order

10-9

cm s-1

, but our simple analysis assumes uniform recession of the solid/liquid

interface and must therefore underestimate the growth rate of the negative dendrites by an

amount that will scale with the volume fraction of porosity within the negative dendrite

zone.

Figure 2.8 Current decay curves for dealloying of Mg0.10Cd0.90 at different temperatures,

with fitted lines in black. The inset is as-interpolated curve of Mg chemical diffusion

coefficient vs. reciprocal temperature

2.4.2 Kirkendall voiding during interdiffusion in Mg-Cd

Chemical diffusion in an alloy with different elements at different rates tends to

accumulate vacancies at the faster diffuser side, which is the case for our Mg0.10Cd0.90

dealloying. As described in the introduction, this system has been examined with regard

to the Kirkendall effect(46); however this early work apparently did not examine the

25

resultant microstructure for voiding. It showed that Mg atoms diffuse ~2 – 3 times faster

than Cd at 210 C implying that vacancies and voids will tend to accumulate on the Mg-

rich side of a diffusion couple. In principle, a similar process should be occurring during

solid-state mass transport controlled dealloying, but the shape of these voids and their

location should be distinct from the negative dendrites described above. In an ancillary

Kirkendall voiding experiment, a 500 nm thick layer of Cd, mimicking a dealloyed Cd-

rich layer, was electrodeposited on to an electropolished Mg0.10Cd0.90 alloy surface.

Figure 2.9 is a FIB-milled cross-section showing that the resultant microstructure

contains nanometer-size isolated voids that mainly accumulate on the Mg0.10Cd0.90 alloy

side of the interface. It is notable that the voids evolved to depths (as measured from the

interface of the diffusion couple) significantly deeper than the penetration depth of the

negative dendrites in dealloyed samples.

Figure 2.9 Cross-section view of the bilayer sample annealed in the Kirkendall voiding

experiment. The scale bar is 1 um

2.5 Conclusions and remarks

As conclusions for this chapter, in Mg-Cd alloy system, we’ve shown that under

percolation threshold of the less noble element, dealloying could proceed by bulk

26

diffusion when its rate is sufficiently high, and negative dendrite voids instead of bi-

continuous structure will evolve correspondingly and the dendrites have preferred growth

direction due to surface energy anisotropy. Additionally Kirkendall voids will form at the

condition of negative dendrite formation.

The same scenario can happen for other low melting point alloys and even high

melting point alloys for small enough particles, owing to Gibbs-Thompson melting point

depression. Another relevant observation exists in LiFePO4 cathode. One report shows

“porosity” formation in chemically de-lithiated LiFePO4(54). Though the one-

dimensional diffusion of Li ions is not in favor of correlating the process to dealloying, a

more detailed examination of the morphology may help to resolve the long debate over

the Li transport mechanism in this material.

27

3 DEALLOYING IN LI ALLOYS

3.1 Background

Among all low melting point alloys, the most interesting and important systems are

those being considered in advanced electrochemical energy storage systems such as

future lithium-ion batteries, including Li-Si and Li-Sn, et al. Despite the numerous

electrochemical and computational studies connected to battery development aimed at

understanding the thermodynamics and mass transport of Li in high mobility host

reservoirs, we are surprised to find out that only a few of these have specifically

addressed dealloyed (de-lithiated) morphologies(55, 56). Most of the commentary related

to porosity evolution is vague and often confused with cracking and fracture issues that

can occur in anode reservoirs owing to the large volume expansions these systems

undergo during lithiation. There are only several reports in the literature linking porosity

evolution in these systems to dealloying and none of these discuss bi-continuous

morphologies(57, 58).

As we now attempt to introduce dealloying theory to Li alloys, the focus is mainly

divided into two parts. Unlike Mg-Cd, the dramatic differences between the components

with respect to atom size, crystal structure and bonding cast doubt on whether the

dealloying theory can be fully applied to Li alloys. We will first access the process by

aqueous free corrosion dealloying, and then examine factors affecting morphology

evolution electrochemically. The second part will on the bulk diffusion’s effect on

dealloying morphology, tested by varying dealloying rate.

28

3.2 Experiments

In aqueous chemical de-lithiation experiments, Li / metal bi-layer samples were

prepared by heating a Li sheet and a metal sheet under external pressure at 100C for 3

hours, all inside the UHP Ar purged glovebox. The samples were then completely de-

lithiated in a water / acetonitrile (Sigma Aldrich) mixture (1:1 v/v) within about 10 mins.

Sn particle electrodes were made by binding commercially available particles to

copper foils. 100 mesh (Alfa Aesar), 1~5 um (Sigma Aldrich) and ~100 nm (Alfa Aesar)

Sn particles were respectively mixed with Super-C45 carbon black (TIMCAL) and

Polyvinylidene fluoride (Sigma Aldrich) in 5:3:2 weight ratios in N-Methyl-2-

pyrrolidone (Sigma Aldrich). The as-mixed slurry was pasted onto a copper substrate

with a thickness between 10~15um (one monolayer of particles), and dried under N2 at

60C, to maintain the size, shape and particle separation. The Sn electrode (a current

collector was beneath for Sn sheets), polymer separator, counter electrode Li sheet

(Sigma Aldrich) and Cu current collector were assembled in sequence and sealed inside a

pouch cell, under Ar protection; 1M LiPF6 in ethylene carbonate / diethylcarbonate (1:1

v/v) (Novolyte), in which the separator was soaked, was used as the electrolyte. All the

polarization experiments were carried out in a three-electrode cell of similar

configuration, with consistent work electrode surface area (Sn mass), and an additional Li

sheet as the reference electrode.

Electrochemical experiments were all performed in Gamry series-G potentio-stats.

Potentiostatic lithiation were done by holding at various low voltages for 10000 seconds

(50ks for Sn sheet and 100 mesh particles); the electrodes were then discharged at 1V vs.

Li+/Li till the current dropped down to about 10mA/g. As for galvanic experiments (C/n),

29

the total charge was obtained by charging a testing cell of the same electrode surface area

within voltage range between 2.5V (1V for capacity fading test) and 0.05V, and the

average total charge was between 890-936 mAh/g (993mAh/g as the theoretical value).

For a C/1 discharging experiment, the current applied was 993mA/g, corresponding to

about 20µA/cm2 assuming average 2µm diameter particles with 200% volume expansion.

We also found charging methods (potentiostatic or galvanostatic) had no impact on the

morphology. Polarization curves were obtained right after a C/2 charging.

To uncover the electrode morphologies, Sn electrodes were taken out the cell and

kept in acetonitrile for overnight to wash off the solid/electrolyte interphase (SEI) layer.

3.2 Aqueous dealloying of Li alloys and bi-continuous structure formation

As an initial assessment of the morphology from delithiation, Li-Sn, Li-Pb, Li-Cd,

and Li-Bi alloys (bi-layer samples) were dealloyed by free corrosion in aqueous solution.

The nanoporous structure shown in Figure 3.1 is the typical morphology obtained via

dealloying. Due to the alloy preparation method, the composition of the alloys would not

be uniform, which yielded a wide distribution of ligament sizes, most apparent in the case

of Sn. Nevertheless, the average ligament sizes for all metals are considerable larger than

those of dealloyed noble metal alloys, because of the faster surface diffusion. The

correlation between the steady state ligament size controlled by surface diffusion and

intrinsic metal property will be discussed in more details in Chapter 4.

30

Figure 3.1 Bi-continuous nanoporous morphologies resulting from free corrosion de-

lithiation of Sn, Pb, Cd and Bi reservoirs in an aqueous electrolyte. The scale bars in the

images are 2 µm.

3.3 Composition dependent morphology in dealloying Li-Sn alloy

In order to understand the factors controlling morphology evolution in these systems,

we chose to focus on Li-Sn alloy as it is still a popular candidate for high capacity lithium

ion anodes and abundant data is available from extensive research on the system.

Alloying, or as described herein, lithiation, was performed at various potentials to

obtain well defined compositions of Li-Sn alloy in particulate Sn electrodes. The alloys

were then dealloyed at 1V vs. Li+/Li.

31

Figure 3.2 (A) voltage-composition curve for Li-Sn modified from a C/20 charging

curve. SEM images and FIB cross-sections of (B, C) Li0.30Sn0.70, the inset is the

magnified cross-section by 2 times; (D, E) Li0.48Sn0.52; (F, G) Li0.77Sn0.23. The scale bars

are 500nm.

As shown in Figure 3.2, Sn particles containing 30 at% Li or less showed no evidence

of bi-continuous porosity formation, which can be viewed as the parting limit of this

system. While the dealloying was carried by bulk diffusion, the absence of negative

dendrite structure as seen in dealloying Mg0.10Cd0.90 is most possibly due to grain

boundary formation, which will be discussed in session 3.6. On the other hand,

Kirkendall voids which were convoluted with negative dendrite in the case of

Mg0.10Cd0.90 are now apparent.

32

At concentrations of order 50 at% Li, porosity is evident. Additionally, close

inspection of Figure 3.2E shows that the dealloyed particle has a partial hollow-core

structure that developed owing to plastic collapse of ligaments where new grain

boundaries are also present. This type of structural evolution has been seen before in

NPG annealed at the same homologous temperature as room temperature for Sn (see

session 4.2.3 for further discussion). Figure 3.2G shows that for Li concentrations larger

than ~ 70 at% a bi-continuous morphology similar to that in NPG evolves. The difference

in the ligament/pore size apparent by comparison of Figure 3.2E and G is a result of the

difference in starting composition of the alloy, which has been seen in case of Ag-Au

alloy dealloying.

3.4 Particle size dependent morphology in Li-Sn alloy

There are also effects on the dealloyed morphology connected to the physical size of

the reservoir. Figure 3.3 shows how sample size alters morphology under otherwise

identical conditions. For Sn particles of order 2um in diameter originally containing

~70at% Li, dealloying yields a ligament size of order 100 nm but for particles of diameter

less than ~ 300 nm porous morphologies do not evolve. This is in analogy to behaviors

observed on dealloying of noble metal alloy nanoparticles. That is, for particle diameters

less than ~2-3 times the ligament size dealloying does not produce bi-continuous

morphologies.

33

Figure 3.3 The effect of particle size on dealloyed morphologies

Figure 3.3 also shows that as the reservoir size increases the length scale in the porous

structure increases. For large particles and planar Sn sheets the porous length scale is ~

500-700 nm which is similar to that shown in Figure 3.1. We believe that this difference

in length scale is related to the stability of the SEI layer, as illustrated in Figure 3.4. This

layer has the effect of reducing the coarsening rate of the porous structure by reducing the

rate of surface diffusion. During lithiation there is about a 260% increase in the reservoir

volume(59) independent of reservoir size. However, the displacement associated with this

volume change scales with the reservoir size resulting in a larger degree of SEI layer

deformation and corresponding mechanical destabilization of this layer. This tends to

reduce the effect of the SEI layer on coarsening. The reason why the small ligaments

were stable against in-air coarsening after SEI was dissolved is believed to be the oxide

layer formed during the dissolution SEI in the acetonitrile. The interpretation was also

confirmed when we utilized it to fabricate a bi-modal nanoporous Sn sheet. The sample

was prepared by two cycles of potentiostatic charging/discharging, first at 0.4V/1V and

second at 0.2V/1V. In Figure 3.4, the larger level porosity contains ligaments of 1um size,

34

and the smaller level porosity is around 100nm, which was stable against coarsening

since the new SEI formed in the second cycle remained conformal on the ligaments.

Figure 3.4 Bi-modal porous Sn sheet obtained after two potentiostatic cycles

3.5 Dealloying rate dependent morphology in Li-Sn alloy

Dealloying rate effect was studied by discharging Sn particles at various C rates

(Figure 3.5A and B). The effect of de-lithiation rate on morphology evolution in Li-Sn is

shown in Figure 3.6A~D. At a discharge rate of 10C and 1C, the bi-continuous length

scale is similar to potentiostatic discharging and for a C/2 rate this length scale increases

to about 200 nm. At a C/10 discharge rate the dealloyed particle morphology is not bi-

35

continuous, which is interpreted as a case of passivation by surface diffusion. When

alloys with minuscule lattice diffusion are dealloyed at too low a current density

compared to the surface diffusion rate, that is, below critical potential, a compact layer of

the more-noble element forms that results in a passivation-like process that quenches

dealloying; in low melting point alloys like Li-Sn, the low dealloying rate maintains via

bulk diffusion through the Sn rich layer.

Figure 3.5 (A, B) chronopotentiometry curves and (C, D) polarization curves without

and with normalization, respectively

The chronopotentiometry data for the C, C/2 and C/10 discharges demonstrates that

the voltage profiles are nearly identical, indicating that at equivalent remaining Li

contents the alloy surface compositions were similar despite the differences in

36

morphology. We conclude that at these discharge rates solid-state diffusion is sufficient

to compositionally homogenize the particles during dealloying. In order to investigate

how this happens, we examined the dealloying polarization curve behavior at different

sweep rates and scaled the current by the square root of the sweep rate. For mass-

transport limited de-lithiation, the scaled wave peak heights should be independent of the

sweep rate(60). Figure 3.5C shows this data for sweep rates of 5.0, 0.50, 0.25, 0.05 mVs-1

.

The waves in the polarization curves correspond to de-lithiation of Li-Sn phases initially

present and evolving on the electrode surface during potential scanning. These sweep

rates result in de-lithiation times approximately equivalent to discharge rates of 10C, C,

C/2 and C/10 respectively for which bi-continuous morphologies evolve for all but the

lowest sweep or discharge rate. Except at the highest sweep rate, we observe scaling of

the wave heights of all the waves except for that labeled 1. Since a bi-continuous

morphology cannot evolve under conditions of solid-state mass-transport limited

dealloying, we associate porosity formation at the 0.50 and 0.25 mVs-1

sweep rates with

this wave. This conclusion is confirmed by results of potentiostatic de-lithiation

experiments that demonstrate the formation of a bi-continuous nanostructure at 0.5 V

(Figure 3.6E). The second large wave labeled 2 in the polarization curves is associated

with de-lithiation of the ligaments comprising the bi-continuous morphology that evolved

during the first wave. There is no second level of porosity that forms within the

ligaments owing to the size effect previously discussed. For the 5 mVs-1

sweep rate these

waves become convoluted and good sweep rate scaling of the peak heights is no longer

apparent indicating that the bi-continuous morphology is evolving throughout the entire

polarization curve.

37

Figure 3.6 (A~D) Sn particles dealloyed at rates of 10C, C/1, C/2 and C/10 respectively;

(E) particle dealloyed at fixed potential of 0.5V; (F) cartoons illustrate the morphology

evolution at different rates, with the coloring for different alloy compositions.

3.6 Grain boundary formation during lithiation / de-lithiation

In a few of the above images (e.g. Fig. 3.3 and Fig. 3.6D), there are large numbers of

grain boundaries present which were absent in the initial Sn substrates (Fig. 3.7 as

examples). It’s not surprising since in the case of silicon, lithiation could completely

destroy the crystallinity of the solid. We believe this process is more likely to happen

during lithiation as the huge volume increase may impose a large stress to drive grain

growth. The biggest effect from the grain boundary formation to the morphology

evolution is the negation of the void dendrites during lattice diffusion supported

dealloying, even at high dealloying potential (Fig. 3.7b). The grain boundaries will serve

as shortcuts to lattice diffusion and thus consume the vacancies generated by de-lithiation.

38

Figure 3.7 Grain size comparisons between virgin Sn substrates and Sn after lithiation /

de-lithiation circle for (a, b) Sn particles, and (c, d) Sn sheets. The particle in (b) was

lithiated to 0.6V and de-lithiated at 2.5V, and the sheet in (d) was lithiated at 0.2V and

de-lithiated at 1V

3.7 Improving Sn anode cycle stability by nanoporous structure

The nanoporous structure preparation method here can be adopted towards various

applications. In particular, it has a potential to improve the lithium anode capacity and

performance, for all the merits it inherited from the fabrication method. For instance, we

measured in Figure 3.2 the volume change retention from porosity formation. Particles

could retain close to half the volume expansion in the fully charged state, which may

greatly improve its mechanical stability. At the same time, due to its continuous nature,

39

the nanoporous can negate binding materials and even current collector if applied to a

sheet form, and this will help to achieve higher volumetric and gravimetric energy

densities. The way we used to obtain the nanostructure is also facile and more cost-

effective compared to methods employed nowadays to improve the anode performance.

Figure 3.8 Capacity retention tests for different Sn particle electrodes

We made an initial attempt to demonstrate the benefit of the in-situ prepared

nanoporous structure by examining particulate Sn electrodes. Here umSn, NP umSn and

nmSn separately stand for electrodes containing 1~5um diameter Sn particles, 1~5um

diameter nanoporous Sn particles and 100nm diameter Sn particles. The NP umSn

electrode was obtained from umSn by potentiostatically charging and discharging it at

0.2V and 0.8V respectively. The tests were carried at rate of C/2, with voltage cut-off

between 1V and 0.05V. Figure 3.8 shows there is a significant improvement from

40

nanoporous Sn particle. The capacities of both umSn and nmSn faded gradually to as low

as 200 mAh/g after 30 cycles, similar to previous reports. As for NP umSn, the retention

slowed down after 20 cycles, and stayed above 1/3 of the theoretical capacity until the

end of the test. Although this value is far from practical satisfactory, it approached the

better values reported for pure Sn(61, 62). In addition, no attempt was made to optimize

the electrode configuration from the one designed for morphology study, therefore we

believe this facile in-situ method can be applied to further improve the alloy based Li

anode’s performance.

3.7 Conclusions

We show for the first time how well dealloying theory can be applied to Li alloy

systems. The bi-continuous porous structure is obtained for various low melting point

alloys, and in Li-Sn, the morphology evolution depends on alloy composition and particle

size and dealloying rate. Bulk diffusion supported dealloying occurred when surface

diffusion outcompetes dissolution rate; it did not produce negative dendrite structure due

to grain boundary formation and/or surface diffusion.

41

4 DEALLOYING THEORY: REVISITED

In previous two chapters, we successfully incorporated the solid-state mass transport

process into the dealloying theory by studying Mg-Cd and Li alloys. In addition, the

studies extend important factors to unexplored regions, which include surface diffusivity,

crystal structure and composition. We also expect our work to stimulate new studies to

apply dealloying methods to applications such as solid-state energy storages. All of the

above call for a comprehensive review of dealloying theory, which unfortunately does

not exist. In this chapter we will attempt to fill this vacancy with a brief summary of the

central issues of dealloying, as well as to offer interpretations that apply to all dealloying

processes.

As there have been very good reviews on mechanical properties(63) and catalysis

applications for dealloyed nanoporous metals(24), the chapter will be centered around

other fundamental aspects. The first part is on the electrochemical responses during

dealloying, with a special emphasis on their critical behaviors, and the second half is

about the details of morphology evolved during dealloying and coarsening.

4.1 Critical behaviors in dealloying

“Critical” is defined by Merriam-Webster as, relating to or being a state in which

some quality, property, or phenomenon suffers a definite change. In dealloying, the

“change” can be phrased as following: the start of a sustained selective dissolution

process and a concomitant bi-continuous morphology evolution from a macroscopically

flat surface. Criticality in dealloying derives from percolation, but it is heavily affected

by kinetics (e.g. surface diffusion) which obscures the underlying physical connection to

42

critical phenomena in the strict sense. Therefore our discussion on “criticality” here

should be viewed as “critical-like” behaviors.

The word “critical” really only appears with respect to a dealloying “turn-on”

potential or critical potential and this is mainly for historical reasons connected to

literature in corrosion. Nevertheless, I believe the concept is applicable to other

phenomena in dealloying, which includes parting limit and critical alloy size for porosity

evolution.

4.1.1 Passivation

In a binary alloy ApB1-p, the electrochemical redox potential of A can be obtained

from the Nernst equation

4-1

is the standard potential of A, is the gas constant, is the temperature in K, is the

charge transfer number associated with A redox, and and are the activities of A

in the alloy and electrolyte respectively. Whenever the voltage is higher than that in

Equation 4-1, the inability of sustained dissolution of A component should be termed as

passivation. In certain electrolytic condition, a pure metal can also passivate (e.g. forming

oxides), but in dealloying, the passivation comes from the more noble component. Its

effect can be visualized as layers of B atoms on top of the alloy, either forming a near

complete coverage to isolate electrolyte (under parting limit)(64, 65), or leaving pinholes

that are so tiny that extra energy needs to be paid to forward the dealloying (below

critical potential)(14, 22). The passivation persists as assuming no solid-state atomic

movement, and a full coverage conformal layer of the more-noble component. These two

43

properties of the passivation layer give the dealloying sharp turn-on instead of gradual

transition, which is exhibited as criticality.

Percolation theory provides a lower compositional bound of this behavior by

assuming a stationary interface during porosity formation; in real systems, surface

diffusion elevates the critical point because of the tendency of smoothening surface

fluctuations. Either with or without surface diffusion, dealloying will still proceed for a

limited depth prior to passivation(14), as long as applied potential is larger than that

predicted by Equation 4-1. This is termed as surface dealloying, which can be significant

in small sample size electrodes.

When the lattice diffusion rate becomes significant compared to the dissolution rate,

passivation as such no longer occurs. The less noble component rich surface layer will be

quickly homogenized and this process continues as dealloying proceeds. Therefore, the

cases previously categorized as passivation are turned into bulk diffusion controlled

dealloying, and sharp transitions do not exist.

4.1.2 Parting limit

The parting limit is the compositional threshold of the less noble component below

which dealloying cannot proceed without the support of solid-state mass transport. The

name comes from the macroscopic separation or “parting” of gold from alloys like Ag-

Au and Cu-Au. In those two systems, the thresholds are around 55 at% of the less noble

component, while for other alloys such as Al-Cu and Zn-Cu the numbers seem to be

closer to the percolation threshold 20%. In previous chapters, the morphology

44

examinations give ranges for parting limits in Mg-Cd and Li-Sn, and all the above

numbers are listed in Table 4.1.

Table 4.1 Parting limits for various alloys

Alloy System Parting Limit (at%) References

Ag-Au 55 (4)

Cu-Au 50~60 (3)

Zn-Cu 17~20 (6)

Al-Cu 11~16 (6)

Mg-Cd 15~45 Chapter 2

Li-Sn 30~48 Chapter 3

As discussed earlier, the lowest less noble metal content for bulk dealloying should be

set by the percolation threshold, which is about 20~30 at% for cubic and hexagonal

crystal structures. This number can be altered depending on ordering, composition

inhomogeneity and atomic size difference. However, the biggest deviation is in the most

ideal system Ag-Au in the sense that none of the above factors is heavily involved. The

cause has been under debate for a long time, and a recent work by Artymowicz et al.(33)

revisited the concept of high density percolation proposed in 1988 by Sieradzki et al.(19).

High density percolation refers to a percolation process where each of the Ag atoms that

are in the percolation backbone have at least m near-neighbors that are also Ag.

Artymowicz et al. evaluated all the high density thresholds relevant to fcc lattices

(2 m 12) and compared them to the experimental parting limit of Ag-Au. The found

that the threshold for m=9 compared nicely to the experimental result. At concentration

lower than 55at% Ag, even though the Ag atoms percolate, the free volume created by

cluster dissolution isn’t large enough to allow for ion solvation.

45

We also note that all the measurements of parting limits except that of Ag-Au have

been “outdated” because the definitions of critical behaviors described in session 4.1.1

were never followed during the measurements. Thus new examinations will be necessary

to complete the discussion.

4.1.2 Critical potential

For dealloying, the critical potential is one of the most studied features initially for its

benefit to corrosion resistance. The value of critical potential increases with decreasing

less noble component content (until the parting limit), and differs among alloy systems.

Unfortunately, a comprehensive set of values only exist for Ag-Au(4).

The origin of critical potential is most successfully explained in the framework of

percolation theory. In an ideal solid solution ApB1-p, the average cluster size for the less

noble A component can be estimated as(21)

4-2

where is the nearest neighbor spacing. The size marks the initial diameter of the pits at

the dealloying front, which adds a Gibbs-Thompson free energy term of

. Combined

with Equation 4-1, we can reach to the expression of critical potential as

(

)

4-3

Here again, is the interface energy and is the molar volume of the alloy. In addition,

a kinetic term associated with surface diffusion will be present to further elevate the

critical potential(4). Equation 4-3 gives accurate predictions on the critical potential

46

differences among vary alloy compositions, proved by the work in Ag-Au as well as

multilayer Ag/Au samples with manipulated “cluster” sizes(22).

Besides alloy composition, there are other factors significantly affecting the critical

potential. For alloys all containing 75at% less noble component, Cu-Pt and disordered

Cu-Au show ~100mV higher critical potentials than Ag-Au. This difference is believed

to be from the bonding energy, i.e. the term in Equation 4-3. The critical potential of

ordered Cu3Au alloy was measured to be 250 mV higher than disordered Cu0.75Au0.25,

which cannot be fully covered by the ordering energy; instead, if the cluster size is

calculated by the thickest stacking Cu layers in the ordered crystal structure, rather than

the random percolating cluster, the difference can be well explained.

Finally, we discuss effects from significant lattice diffusion. The critical potential

should still be quite distinguishable because it separate two types of current-voltage

behavior — below the critical potential current density quickly goes independent of

voltage into mass-transport control (decays with ⁄ ) and above the potential it turns to

Bulter-Volmer type behavior. However, the measurement of the critical potential will be

significantly altered. As for alloys without solid state mass transport, both polarization

and potential-holding have been applied to obtain critical potentials(4, 13). But polarizing

a low melting point alloy will result in a passivation layer that might increase the critical

potential or even suppress the bi-continuous structure evolution as in the C/10 dealloying

of Li-Sn alloy. Therefore, critical potential measurement can only be performed by

potential-holding when bulk diffusivity is high.

47

4.1.3 Critical electrode size

As shown earlier in 3.4, there exists a size threshold below which bi-continuous

porous structure does not evolve. Compositional analysis shows that dealloying of noble-

metal particles below the size threshold results in noble-metal shell and alloy core

retaining parent alloy content, corresponding a passive state(27, 66). So the critical

electrode size is both electrochemically and morphologically a similar concept to the

critical potential and the critical composition (parting limit).

The cause of the critical size is yet to be explored. We discuss two speculations as

follow. The first is that the appearance of the critical size is due to the increase of surface

diffusivity, because smaller size particles tend to generate more defect sites (step and

kink) on the surface which facilitate the adatom movement. However, one derivation

from this speculation is that ligament size should increase with decreasing particle size,

which is never observed. Moreover, in the case of Sn particles, the critical size (~300nm)

is too large to differ significantly from bulk alloy with respect to defect sites. The second

speculation is drawn in Fig. 4.1. Fluctuations develop at the initial stage of dealloying. By

assuming the surface diffusion’s contribution to passivation is limited to the positive

curvature parts of the fluctuations and the dissolution occurs at the valleys, we can

approximately define a ratio between their areas. In a potentiostatic dealloying

experiment, this number stays constant for a planar alloy whereas it will be decreasing in

particles of a size that is not significantly larger than the fluctuation amplitude that

natively assume to be related to steady-state ligament size (Fig. 4.1A). This will lead to

passivation once dissolution is outcompeted after a shallow dealloying depth.

48

At the same time, we note that even under the critical size, complete dealloying can

occur in cases where potential cycling instead of potential static holding is applied(67,

68). A possible explanation we can offer is that, noble metals such as Pt and Au go

through reversible surface oxidation and reduction in the potential region of cycling, and

this process tends to induce inter- and intra-layer atomic movements that expose the

buried atoms to the electrolyte.

Figure 4.1 (A) cartoon illustrating the difference between planar and particulate alloys,

with dotted lines denoting the effective areas for dissolution and surface diffusion,

respectively; (B) critical size effects on porosity formation in Pt and Au alloys

49

4.2 Morphology characteristics

Dealloyed morphology is often equated to the bi-continuous structure. The is true to a

degree that most of aspects associated to dealloying will be reflected by the details of the

nanoporous structure. The complex combination of these ingredients also acts against an

accurate prediction of properties for a specific bi-continuous structure. The discussion

here will also be centered on the bi-continuous structure. We will try to rationalize the

structural evolution for all dealloying processes.

4.2.1 Theoretical background

Similar as to the critical behaviors, percolation theory provides the basic frame of the

bi-continuous structure. In a binary alloy ApB1-p the cluster size of A in Equation 4-2

limits the smallest pore size one can obtain from dealloying, while the cluster size of B

gives the limit for ligament size. However, all the structures seen in the literatures have

been reconstructed by surface diffusion, and even if a good care is taken, the nanoporous

structure still undergoes rapid coarsening in a short time (12).

It’s clear why surface diffusion acts to smoothen the nanoporous structure, but the

understanding of how it works has not progressed much since Forty’s discussion. A rule

for rough Au surface smoothening based on Herring’s model was directly adopted by

Corcoran et al.(69), described as

4-4

Where and are the final and initial ligament sizes respectively, is the surface

energy, is the surface diffusivity, is the total coarsening time, is the Boltzmann

constant and is the temperature. The value of can be estimated by the mean cluster

50

size of the noble component from Equation 4-1, and it is often a very small number (~1

nm). Undoubtedly this formulation is a simplified description, as the bi-continuous

structure is topologically more complicated than two-dimensional surface roughness. But

it predicts rules of porous morphology evolution that have been constantly confirmed,

such as the dependence for coarsening(70, 71). This type of time dependence results

in a pseudo steady-state length scale, meaning that after it stabilizes within about one day

it takes weeks or longer to double the size(12). In the following discussion, steady-state

ligament size will be used as the representative length scale, instead of the mean pore size

which is harder to be accurately measured.

Another model of coarsening based on solid-state Rayleigh instability was recently

introduced by Erlebacher(34) to explain a surprising observation of encased voids inside

the ligaments(72). The Rayleigh instability is also based on energy minimization, and it

better describes the pinch-off events of the saddle point configurations that maintain the

structure’s self-similarity during coarsening. The process can be explicitly explained by

looking at a slim cylinder. In Fig. 4.3A, longitudinal fluctuations with different

wavelengths will tend to develop at the cylinder surface (interface). Small perturbations

quickly die out, but once the wavelength exceeds its circumference, the cylindrical shape

will not be stable, because the average radial curvature decrease outbalances the

longitudinal curvature increase and the system moves towards a lower energy state. In bi-

continuous porous metal, both the ligament and the pore channel can be viewed as

cylinders and the surface diffusion provides for the mechanism of the instability during

the coarsening.

51

4.2.2 Length scales in bi-continuous structures

As discussed in the previous session, at ambient temperature the ligament size

achieves a pseudo-steady state value after about one day. The parameter used most often

to tune this length scale is the surface diffusivity. It depends exponentially on temperature,

which makes post-annealing a powerful tool. Starting from ~10 nm, the NPG ligaments

can be enlarged to micrometer level by 10 minutes of annealing at 600 C(12), and the

annealing process follows the rule, as long as sintering is not involved. The

temperature effect can also be applied during dealloying, although less tunable due to the

limit of the electrolyte(70).

Another way of controlling surface diffusion can be achieved at the electrode /

electrolyte interface, often along with dealloying. A slight change of electrolyte

composition may greatly affect the nanoporous structure, since the amount of addions

required to cover the surface is small compared to the electrolyte volume. The addition of

halide ions is the most common way to increase the length scale in-situ(26, 69, 73), and

passive surface layers have been used to suppress the surface diffusion controlled

coarsening. Here the passive layers can be metal oxides(74), precipitates(75), and even

SEI layers as shown in Chapter 3.

Depending on the particular alloy (noble-metal, Li-Sn, Mg-Cd) there is a wide

variation in the pseudo-steady state ligament size. We can understand this by

consideration of the surface diffusion. There is an empirical correlation that the activation

energy of surface diffusion is proportional to the metal’s melting point(76). A collection

of nanoporous metal ligament sizes from literatures (Table 4.2) were plotted together

with the porous metals we obtained in Chapter 3 versus their , shown in Figure 4.2.

52

The fitted line crosses all points surprisingly well. Even those with high bulk diffusivity

fit the trend, because all ligament sizes are still far below the point where bulk diffusion

takes over the coarsening process from surface diffusion(77).

Table 4.2 Data used in Fig. 4.2

Parent Alloy Ligament Diameter

(nm) Reference

Ag70Au30 20±10 (78)

Co75Pt25 3±1 (31)

Mn70Cu30 16±4 (79)

Co20Pd80 6±2 (80)

Al77Ag23 35±5 (81)

Figure 4.2 Ligament size and homologous temperature correlation for porous metals

53

4.2.3 Ligament collapsing

During nanoporous metal annealing, one phenomena observed along with ligament

coarsening is the collapse of ligaments (12, 82). It’s similar to sintering, which

annihilates the porosity. The collapse seems occurs at too low a temperature to involve

creep, and the bi-continuous structure is robust enough meaning that the self-weight or

“body force” of ligaments does not seem to be sufficient to cause this behavior.

Figure 4.3 (A) Rayleigh instability in porous metals; (B) ligament collapsing mechanism

at the grain boundary, with ligaments susceptible to collapsing circled in blue; (C) and (D)

NPG with collapsed ligaments after 10 mins and 1 h annealing at 500C, in which the

collapsing starts at grain boundaries and grow on the surface. The scale bars are 40um

To understand the mechanism of collapsing, we refer back to the Rayleigh instability.

The robustness argument for the porous structure is founded on two assumptions for the

ligaments, which are uniform size and high connectivity. The first assumption apparently

does not hold as the Rayleigh instability renders radial distribution along ligaments. The

same process also decreases the ligaments’ connection, which won’t by itself result in

54

any weak points in the bulk because any ligament that loses connections due to pinch-off

will be consumed to enlarge others. However, there are specific sites that may behave

differently. At the surface, ligaments are under-connected compared to those in the bulk;

at the intersection between grain boundary and surface, due to preferential dealloying

induced by composition segregation as well as grooving, ligaments with even fewer

connections exist, as circled out in Fig. 4.3B. One can describe those ligaments as

dangling, borrowing the concept of dangling bond, meaning that they are more likely to

suffer structural change. Once a dangling ligament gets pinched-off, it falls off the

nanoporous network. The repetition of this event accumulates solid clusters, adjacent to

which are more ligaments susceptible to collapsing. The process should occur at any

temperature, but at low temperature accumulation of the clusters might be too slow to be

observable. At elevated temperature, collapsing starts at the grain boundaries on the

surface, and propagates primarily along the surface (Figure 4.3C, D). It may also move

downwards into the bulk, when the temperature is high enough to destabilize all the

ligaments across the surface.

We note that in a nanoporous particle, when the particle size approaches the ligament

size (certainly above the critical size to contain the structure), the ligaments on the

surface are further under-connected due to the particle curvature, therefore more

susceptible to collapsing and forming a core/shell structure, such as what we saw in

Chapter 3.

55

4.2.4 Volume change

During the dealloying process, the massive atomic rearrangement will result in

volume change that can’t be neglected. There is only one systematic examination on

volume change by Parida et al.(83), so to make a comparison we performed

measurements on the porous Sn particles in Chapter 3. Solid / void area ratios at the

cross-section were used to estimate the volume changes, and initial volumes (alloyed

state) were calculated from the theoretical alloy densities. When the bulk diffusion is

taking part in the dealloying as in Figure 4.4, significant volume shrinkage occurs since

fewer vacancies agglomerate into voids. In the case of active surface diffusion alone, the

volume change can be divided into two groups. At fast dealloying rate, such as high

overvoltages for Ag-Au(83) and the potentiostatic dealloyed Li-Sn, almost half of the

volume initially occupied by the less noble metal vanishes, whereas slow-rate-dealloyed

Ag-Au retains its size well(71, 83). While Parida et al. speculated a few operating

mechanism of the volume change, it is still unclear to us what the controlling process is.

Figure 4.4 Volume change in dealloyed Li-Sn alloys

56

4.2.5 Encased voids

A surprising feature and interesting feature in NPG is that of isolated encased voids

within the ligaments (see Figure 4.5A for example). Rosner et al. reported it for the first

time and confirmed their complete encapsulation by tomography(72). As mentioned in

session 4.2.1, Rayleigh stability was employed to explain its formation (34). Because of

the symmetry between ligaments and pore channels, the same pinch-off process can

occur to a pore channel surrounded by solid metal. The as-formed isolated voids will be

morphologically stable since they do not participate in coarsening. In fact, decades ago,

similar types of voids formation have been extensively studied and explained by Rayleigh

instability for metal and ceramic grain coarsening(84, 85).

The interpretation is just the start of an interesting scenario. During the encasing

process, the electrolyte may remain in the encased pore. The encased voids should not be

vacant, but filled with electrolyte. Following this speculation, we carried out careful

Electron Energy Loss Spectroscopy (EELS) analysis to trace the oxygen signal inside the

voids in an NPG dealloyed in concentrated nitric acid, and the results are shown in Figure

4.5. Despite the strong shielding effect from the Au shell, significant oxygen signals

absent in other part of the NPG were detected in large encased voids. We believe this is

strong evidence that we’ve obtained a metal-shell / solution-core structure.

57

Figure 4.5 (A) Encased voids in NPG and (B, C) EELS scans across voids indicating

significantly higher counts of oxygen signals inside the voids

While it may require other characterization methods to confirm the existence of the

electrolyte, the structure could have a wide range of applications if realized in a

nanoparticle. We note there have been reports on hollow nanoparticle structures prepared

by galvanic exchange(86, 87), and although researchers usually refer to bulk diffusion

and Kirkendall voiding to explain the morphology, we suspect the so-claimed hollow

core should be as well filled with electrolyte.

58

5 FROM DEALLOYING TO DECOMPOSITION

5.1 Background

So far in my dissertation, I have discussed the behaviors of a broad spectrum of

alloys with dramatically different chemical and physical properties. A radical question to

pose is that, what if we change one component in the binary alloy to a non-metal For

example, what morphology would one observe by selectively removing oxygen from a

metal oxide? We will term such a process as decomposition and in analogy to dealloying,

vacancy formation should evolve due to component dissolution.

This type of process in fact has been studied before in the electrolysis process, where

people realize that without a porous layer formation, electrolysis of metal oxides or

halides cannot advance into the bulk solid (88, 89). Others have also prepared porous

structures in small size scale materials following the argument(90). However, no

connection has been established between decomposition and dealloying. In this chapter,

we will give a preliminary discussion of this process as well as briefly consider the

similarities and differences to dealloying.

5.2 The formula of bi-continuous structure evolution from decomposition

Selectively leaching one component from a compound cannot be achieved without a

state change of the other. Taking compound AxBy (A is a metal element, x and y are both

integers) as an example, unlike the dealloying process, the remaining component A is the

one with electron transfer, written in the form as

5-1

59

Here the compound can be Ag2S, SnS, or even CuSO4, all of which will be examined

later. Due to the limited solid-state conductivities of the compounds, electrochemical

decomposition may bring further complications, as the ionic conduction can become the

RLS. This problem can be solved by the introduction of reducing agent such as NaBH4 to

carry out Reaction 5-1 chemically. The chemical reaction will need to be faster than the

solid-state bulk diffusion, because similar as discussed in Chapter 2, if the RLS lies in the

shrinking compound phase, the solid / solution interface will not be stable.

While the discussions above are limited to the solid-to-solid phase transition pathway,

reactions of solid compounds through corresponding solvated species have been

considered to be the dominating paths at least when it comes to electrochemical

reductions. For example, AgCln(n-1)-

always acts as an intermediate ion when AgCl is

electrochemically reduced to Ag(89, 91), and the reduction is restrained to the electrolyte

/ AgCl / Ag triple-phase boundary to provide both the reactants and electrons. Although

the location limitation is eliminated in a chemical reaction, the electrolytic pathway could

still heavily participate since it often requires lower energy. However, we argue here that

the pathways will not affect the general bi-continuous morphology, for the following two

reasons. First, the interface will remain macroscopically flat (much larger than the

nanoporosity scale) since all the possible RLS’s are still in the growing phase. Second, as

long as the reducing agent content is much higher than the solvated species, the reduced

product will retain its continuity because virtually all reduction will take place in the very

vicinity of the interface and the rate and amount of the reduction reaction drops sharply

into the electrolyte due to the decreasing reactant concentration.

60

The electrolytic pathway will in fact give us new ways to control the morphology

evolution. In the case of solid-to-solid phase transition like dealloying, the electrode /

electrolyte interface stays sharp with the width of an adatom; whereas in the solvation

and then reduction process, the interface can be viewed as diffusive. In the view of

percolation, a diffusive interface can also be taken as titrating vacancies (filled with

electrolyte) of a gradient concentration to dilute down the initial compound composition.

An apparent result is that compounds that are initially passive against selective

dissolution can be activated to produce bi-continuous structure.

5.3 Experimental

SnS (Precision Chemical), CuSO4*5H2O (EMD) and PbCO3 (Alfa Aesar) were used

as received. Ag2S was prepared by oxidizing a Ag wire in 0.1M Na2S (Sigma Aldrich)

solution at 0V vs. NHE. AgO was deposited by applying a fixed current (0.1mA/cm2 to

1mA/cm2) to a Pt-Ir wire (ESPI metals) in 0.2M AgNO3 (Sigma Aldrich) and 0.05M

NH4OH (Sigma Aldrich) solution. All the compounds except CuSO4*5H2O were reduced

by 0.1M NaBH4 (Sigma Aldrich) aqueous solution, and washed with water afterwards.

CuSO4*5H2O reduction was carried in saturated NaBH4 acetonitrile solution to minimize

the compound’s solubility, and the product was washed with acetonitrile and water in

sequence.

5.4 Results and Discussion

61

The starting compound morphologies are listed in Figure 5.1. They are all granular in

the sense that the size effect we found in dealloying will not enter into the preliminary

examinations.

Figure 5.1 Compounds before de-composition reaction, (a) AgO; (b) SnS; (c) Ag2S

(adjacent to a cross-section); (d) CuSO4

As shown in Fig. 5.2, the reductions of both AgO and SnS result in bi-continuous

structures almost identical to those obtained by dealloying. The length scales of ligaments

also agree perfectly with the points in Figure 4.2, therefore the porous structure

coarsening is controlled by the same surface diffusion process. The structures well retain

62

their initial substrate shapes, indicating most of the phase transition occurred inside the

volume of the starting compound; at the same time we believe the electrolytic pathway

participated the decomposition process, indicated by the filaments of nanoporous Ag

protruding out of the crystalline grains and the rough surface of porous Sn ligaments.

Nevertheless, almost no reduction products were found away from the surface,

confirming the well-contained decomposition process.

Figure 5.2 Decomposed (a, b) AgO and (c) SnS

The reduction of Ag2S surprisingly results in well-aligned nanowires instead of bi-

continuous structure (Fig. 5.3). The Ag wires are of diameter ranging from 100~200nm,

which are comprised of smaller filaments if inspected closely. There are two causes that

may be responsible for this type of highly directional structure — the first one is mass

transport limitation, and the second is anisotropic growth. We believe the solid-state

diffusion in Ag2S is not playing any role here although the compound is famous for its

high ionic conductivity(92), because the diffusion rate cannot yield such a reaction depth

during the experimental time (~1000s). The anisotropy in the crystal structure could

account for the directional decomposition, which will need more investigation, to

correlate the packing density of each orientation to the morphology.

63

Figure 5.3 Decomposed Ag2S

At last, we show that the decomposition processes of salts result in same bi-

continuous structure. In Figure 5.4, though still covered with precipitates, both reduced

CuSO4*5H2O, and PbCO3 yield porous metal structures that are as bi-continuous as

dealloying products. The ligament sizes again agree with the prediction in Figure 4.2.

These results extend the applicability of the decomposition process to a huge volume of

chemicals, therefore give the possibility to further tune the involved parameters like

reactant solubility to study their effects on morphology evolution. Moreover, the paths

towards nanoporous structures become abundant, which greatly benefits the control of

morphology as well as the cost of fabrication.

64

Figure 5.4 Decomposed (a) CuSO4*5H2O, (b) PbCO3

65

6 CONCLUSIONS

1. In a bulk electrode, at sufficiently high overvoltage, regardless of the rate of solid-

state bulk diffusivity, dealloying always results in bi-continuous porous structure

as long as the less noble component composition is above the parting limit.

2. The length scale of the porous metal, i.e. ligament diameter, is controlled by

surface diffusion, and can be correlated empirically to the homologous

temperature.

3. If the less noble component content goes below the parting limit, especially the

percolation threshold, negative void dendrite structure should evolve during the

bulk diffusion controlled dealloying, unless surface diffusion rate is too high or

grain boundary diffusion dominates, in the case of which dealloying produces

only surface roughness. Kirkendall voiding always occurs along with bulk

diffusion controlled dealloying.

4. The negative dendrite shapes will be anisotropic if the more noble component

possesses anisotropic surface energy.

5. There exist a critical size for particulate alloy electrode to contain porosity

evolution, which is usually 2~3 times of the “steady-state” ligament size.

6. Under conditions for which lattice diffusion is significant, low dealloying rate will

not result in bi-continuous owing to the evolution of a surface layer rich in the

more noble component. Dealloying proceeds thorough this layer supported by

solid-state transport.

7. Enclosed voids observed inside NPG ligaments, induced by Rayleigh instability,

contain electrolyte trapped during the surface diffusion controlled encapsulation.

66

8. The correlation between morphology and its controlling kinetics in dealloying can

be extended beyond dealloying, to other interfacial controlled morphology

evolution. For example, selective dissolution of elemental components in

compounds can result in bi-continuous structures as well.

67

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